At any instant the velocity of a particle of mass 500g is (2t ^ i +...

The equation for velocity is

\overset{\to}{v} = \left(2t\overset{^}{i} + 3{t}^{2}\overset{^}{j}\right)

Thus, the acceleration is

\overset{\to}{a} = \dfrac{d\overset{\to}{v}}{dt} = \dfrac{d ( 2t\overset{^}{i} + 3{t}^{2}\overset{^}{j} )}{dt} = \left(2\overset{^}{i} + 6t\overset{^}{j}\right)

At $t = 1s$, \overset{\to}{a} = 2\overset{^}{i} + 6\overset{^}{j}

The force is written as \overset{\to}{F} = m\overset{\to}{a} = \dfrac{2\overset{^}{i} + 6\overset{^}{j}}{2} = \overset{^}{i} + 3\overset{^}{j}

Comparing it with the given value of force, $x = 3$.